Disclosure: Actually posted January 17, 2014, originally scheduled for December 31, 2013 as that month's "Free/Low-Cost Anime Pick", hence the date. My apologies…
While I try to avoid popular titles for Free/Low-Cost Anime Pick of the Month (particularly current titles), I may make an exception for those of note (see the Monogatari Series and Little Witch Academia). This is one of those exceptions, as well--only this time, I am highlighting two series that I feel are showcasing the power and potential of animation at its highest level, albeit in two very different ways.
KILL la KILL
Official Sites: Japanese, English
Additional Links: ANN Entry, MAL Entry
Video: Crunchyroll*, Hulu, DAISUKI*, Aniplex Channel
*Multi-language subtitle options available
The first of these is perhaps second to only Attack on Titan as the most rabidly-popular title of 2013: KILL la KILL. From the very moment it was announced, it was certainly the most anticipated title around, and it has not fallen short of that hype since its October debut. It is Hiroyuki Imaishi's first full directorial work at his new studio, TRIGGER, since leaving GAINAX (whose first work was the aforementioned LWA), and true to the sheer creative potential and imagination it possessed, it is as artistically-free as one might hope.